Volume 40, Issue 5, 01 March 1964
Index of content:
40(1964); http://dx.doi.org/10.1063/1.1725294View Description Hide Description
The attraction forces between large molecules having highly mobile electrons distributed over many atoms are not well understood. The Coulombic interaction between electrons within a molecule causes the motion of each mobile electron to be correlated with those of many other electrons of the molecule. These correlation effects modify the attraction forces. A proper assessment of these effects at present is extremely difficult, and usually impossible to do. In this paper we calculate the ``mobile electron'' attraction force between long, equal bond polyenes (one of the most simple examples of large molecules having mobile, distributed electrons), and use the Tomonaga method to assess the correlation effects. We compare our results with those of earlier investigators who used an ``independent electron'' model which ignored correlation effects. We find that correlation effects are very important—their neglect leads to significant overestimation of the attraction. We give a simple physical interpretation of our results. Many of our conclusions should be applicable to other large molecules, such as the polyacenes.
Exchange Rates by Nuclear Magnetic Multiple Resonance. III. Exchange Reactions in Systems with Several Nonequivalent Sites40(1964); http://dx.doi.org/10.1063/1.1725295View Description Hide Description
The nuclear magnetic multiple resonance method for the study of chemical exchange rates has been applied to systems in which a nucleus X is reversibly exchanged between three nonequivalent sites. A procedure is outlined, which is applicable to systems with any number of sites and permits the determination of the lifetime τ K at any one site K. In this procedure the effective ``relaxation time'' τ1K and the equilibrium z magnetization, M 0 K (τ1K /T 1K ), are determined in experiments (Type I) in which the X signals at all other sites are completely saturated. The rate constants λ KL and λ LK of the individual exchange reactions (K⇄L) may then be determined in Type II experiments in which the signals of all sites excluding K and L are saturated. In Type II experiments only the equilibrium signal intensities need be measured.
The method has been applied to the base‐catalyzed proton exchange in the keto—enol system of acetylacetone and it was found that exchange between the olefinic =CH and hydroxylic —OH protons occurs merely as a consequence of the keto—enol transformation. Within the accuracy of the measurements no evidence was found for a proton exchange between the =CH and —OH protons which does not involve the CH2 group in the keto form as an intermediate.
On the Structure of the Three‐Particle Scattering Operator in Generalized Boltzmann Equation for Homogeneous Gases40(1964); http://dx.doi.org/10.1063/1.1725296View Description Hide Description
It is shown that the weak‐coupling version of Bogolyoubov theory in a form recently derived leads to a three‐particle term in the equation of evolution of the velocity distribution function, in which the finite duration of collisions is taken into account in a way strictly equivalent to the Prigogine theory in the Markovian approximation.
40(1964); http://dx.doi.org/10.1063/1.1725297View Description Hide Description
The method of obtaining vibronic selection rules is described for an isolated impurity rare earth or actinidetype ion in a rare earth or actinide salt for various symmetry points of the Brillouin zone. The method is applied to Pr3+ in LaCl3 and the results used to further interpret the vibronic spectrum previously reported by Richman, Satten, and Wong. It is shown that in addition to the region around k=0, the region about the plane kz =0 is also probably the most important for the vibronic transitions. The points K and K′ are shown to lead to the same type of spectrum as the point at k=0.
40(1964); http://dx.doi.org/10.1063/1.1725298View Description Hide Description
Measurements of the diffuse reflectance spectrum of K3CrO8 and its dilutions in CaF2 essentially support the transmission results of Swalen and Ibers. Peaks observed at 2.00 and 2.53 eV are attributed to d—d transitions on the Cr5+ ion, others at 3.35 and 5.00 eV to charge transfer. A crystal field analysis yields a Dq value of 0.41 eV for the Cr5+ ion, a result consistent with that obtained from the spectrum of the hypochromate ion, 0.45 eV.
Inelastic Scattering of 390‐V Electrons by Helium, Hydrogen, Methane, Ethane, Cyclohexane, Ethylene, and Water40(1964); http://dx.doi.org/10.1063/1.1725299View Description Hide Description
Electron impact spectra obtained by the inelastic scattering of 390‐V electrons from helium, hydrogen, methane, ethane, cyclohexane, ethylene, and water are given. It is shown experimentally that, at small scattering angles and a fixed velocity‐analyzer setting, the scattered current as a function of pressure contains a maximum. The theory of this effect is discussed.
Theoretical Calculation of Electron Collision Cross Sections for the 1 1 S→2 1 P Transition in Helium40(1964); http://dx.doi.org/10.1063/1.1725300View Description Hide Description
40(1964); http://dx.doi.org/10.1063/1.1725301View Description Hide Description
Inelastic electron collision cross sections at small scattering angles are determined for molecular hydrogen using electrons whose initial kinetic energies range from 324 to 461 V. Oscillator strengths have been calculated from the data and compared with values determined from ultraviolet absorption data by other investigators. The oscillator sum has been calculated and compared with theory and calculated refractive indices compared with experiment. Agreement is good.
40(1964); http://dx.doi.org/10.1063/1.1725302View Description Hide Description
An apparatus for the study of inelastic electronic collision cross sections of molecules as a function of scattering angle is described. The accuracy of excitation potential and collision cross section measurements is illustrated by means of examples involving helium, carbon monoxide, and oxygen.
40(1964); http://dx.doi.org/10.1063/1.1725304View Description Hide Description
Electron collision cross sections at three voltages have been determined for two transitions in nitrogen. One of these corresponds to the Lyman—Birge—Hopfield bands, a forbidden system, and it is shown that the collision cross sections are compatible with the term symbol assignment for the excited state.
40(1964); http://dx.doi.org/10.1063/1.1725305View Description Hide Description
Electronic Collision Cross Sections and Oscillator Strengths for Oxygen in the Schumann—Runge Region40(1964); http://dx.doi.org/10.1063/1.1725306View Description Hide Description
Electron collision cross sections have been determined for that transition in oxygen corresponding to the dissociation continuum of the Schumann—Runge bands. Generalized oscillator strengths have been calculated from the data and extrapolated to zero momentum change for the colliding electron. The extrapolated value obtained, when integrated over the transition, is 0.230. This value is compared with oscillator strengths obtained from ultraviolet absorption spectra by other investigators.
40(1964); http://dx.doi.org/10.1063/1.1725307View Description Hide Description
Additional data on the cross sections for the 1 1 S→2 1 P transition are reported and compared with extended theoretical calculations. Some additional results on the 1 1 S→2 1 S transition are also reported.
Collision cross sections and oscillator strengths have been determined for several excitations in the ionized continuum. Oscillator strengths agree well with theory except in the vicinity of the double electron excitations. Two peaks which involve simultaneous excitation of two electrons have been observed. A discontinuity in the ionized continuum on passing through a peak corresponding to a double excitation has been observed.
40(1964); http://dx.doi.org/10.1063/1.1725308View Description Hide Description
An electron source is described that provides, by means of an electrostatic velocity analyzer, for velocity selection on an electron beam before scattering. The energy width of the electron beam is sufficiently reduced to resolve the transitions to the 5 1 P and 6 1 P states in helium. These states are separated by 0.17 V. Relative oscillator strengths for two additional members of the Rydberg series 1 1 S→m 1 P have been determined by study of the zero angle electron scattering.
Integrated Intensity Measurements of the 1.9‐μ Bands of CO2 in the Temperature Range 1400° to 2500°K40(1964); http://dx.doi.org/10.1063/1.1725309View Description Hide Description
Measurements have been made of the total integrated band intensity of the 1.9‐μ bands of CO2 in the temperature range 1400° to 2500°K. The gas was heated to the high temperature by a shock wave reflected from the rigid end plate of a shock tube. The experiment determines the total integrated band emission as a function of optical path length. The total emission is related to the integrated band intensity in a simple way.
The intensity in the 1.9‐μ region of the CO2 spectrum arises from three combination bands, namely the (v 3+4v 2), (v 3+2v 2+v 1), and (v 3+2v 1) bands. These band systems are in strong Fermi resonance. The bands have not been resolved; the total integrated intensity of the three bands was measured as a function of temperature. The temperature dependence of the absolute intensity is discussed in terms of a simple model using the harmonic oscillator approximation to the CO2 molecule. The results indicate that the intensity in the 1.9‐μ resonant triplet of CO2 originates in the (v 3+2v 1) band. An extrapolation of the data using the derived temperature dependence gives an integrated band intensity of 2.07 (cm—2 atm—1) at STP for the total 1.9‐μ CO2 band.
40(1964); http://dx.doi.org/10.1063/1.1725310View Description Hide Description
This paper discusses the possibilities of obtaining useful information from so‐called ``metastable lifetime'' measurements. An approximate method is described for computing the ratios of parent‐ion to metastable peak intensities via the statistical theory. The predictions of the statistical theory are compared with those of models employing a small number of discrete rate constants. It is shown that, in certain instances, it is possible to determine which model is correct by performing experiments as a function of ionizing voltage. Data for the 30.4 and 31.9 metastables of n‐butane, and the 56.1 metastable of benzonitrile appear to substantiate the validity of the statistical theory.
40(1964); http://dx.doi.org/10.1063/1.1725311View Description Hide Description
The probabilities of dissociationP dis, excitation P ex, de‐excitation P de, and the associated average energy exchanges were calculated theoretically for a highly energized, anharmonic oscillator (I2 or Br2) colliding classically with an inert gas atom C through a Morse‐type potential. The effect of varying mass and well depth was investigated.
It was found that the effect of anharmonicity is to favor excitation and dissociation. However, the average ΔEv for these processes is about the same for harmonic and anharmonic oscillators and not much bigger than 1 to 2 RT. P dis increases markedly with increasing mass. The well depth (V 0) does not seem to have much effect in the range 0.004<V 0/D 0<0.14, where D 0 is the bonddissociation energy.Exchange reactions are observed, but for shallow well depths they are rare events. From the results, it is possible to calculate λ, the probability of stabilizing an atom pair by a third‐body collision. This turns out to be independent of temperature but depends strongly on the mass of the third body C. It is always in the range 0.1<λ<1.0 for the systems considered, and increases with increasing mass of C.
For the dissociation process, it is found that the average dissociation event gives rise to a pair of atoms with very little excess energy (∼0.10 RT) above the dissociation barrier. This implies an activation energy for dissociation of the order of D 0°—2RT in the Benson—Fueno theory and also a T —2 dependence for the rate of recombination of atoms.
40(1964); http://dx.doi.org/10.1063/1.1725312View Description Hide Description
The molecules vaporizing from graphite at 2300° to 2600°K have been trapped in neon, argon, and xenon matrices at 4° and 20°K. The near‐ultraviolet bands of C3, beginning at 4050 Å in the gas, have been observed in the absorption spectra of these matrices but shifted to 4057 Å in neon, 4102 Å in argon, and 4226 Å in xenon. The neon spectrum is strikingly similar to low‐temperature gaseous spectra, including cometary spectra, but the matrix bands occur in groups about 100 cm—1 wide. The infrared spectrum yields a strong band at 2038 cm—1 in argon (2042 cm—1 in neon) which is assigned to v 3″, the asymmetric stretching frequency of C3 in the ground electronic state. When the argon matrix is allowed to warm up, diffusion occurs, and larger carbon molecules, C4, C5, C6, etc., are formed, causing the appearance of many new bands in the infrared. The Swan bands of C2 are observed in neon and argon matrices, but only after some annealing of the matrix has occurred by warming. The vibrational frequency of C2 in the excited 3Π u state in a neon matrix is 2094 cm—1, exceeding the value found in any other matrix or in the gas (1750 cm—1). The possible appearance of C2 in its 1Σ g +ground state in neon and argon matrices is briefly discussed.
40(1964); http://dx.doi.org/10.1063/1.1725313View Description Hide Description
The vaporization of C13‐substituted carbon has established the isolation of C3 molecules in the matrix and the assignment of the v 3″ frequency observed in the infrared spectrum. A vibrational analysis of the near‐ultraviolet spectrum (the well‐known 4050‐Å gas bands) of C3 trapped in a neon or argon matrix has been carried out. The presence of a large Renner effect (ε=+0.566) in the bending motion in the excited state of this 1Π u ↔X 1Σ g + transition has been confirmed. Infrared and fluorescence spectra also support the assignment of a low bending frequency (∼70 cm—1) in the ground state as recently proposed by Gausset, Herzberg, Lagerqvist, and Rosen. Then the following vibrational frequencies apply: v 2″ is still doubtful because it does not yield thermodynamic functions for C3 which agree with those derived by mass spectrometry. The f number (oscillator strength) of the 0–0 band has been found to be about 7×10—4 in a neon matrix. The properties of a long‐lived emission (lifetime=0.02 sec in neon) at 5856 Å indicate that it is the 3Π u →1Σ g + transition of C3. Another, rather unpredictable, system of bands near 4200 Å has also been seen in absorption and emission, but the molecule producing these bands has not been identified. An attempt has been made, via a linear chain model, to assign the stretching frequencies of the larger carbon molecules, C4, ···, C12, which have been observed in the infrared after solid‐state diffusion was allowed to occur.